Standard to Vertex Vertex from Standard Form Equation
The Standard form of an equation is y=ax^2+bx+c The Vertex form of an equation is y=a(x+h)^2+k Ex. 1
y=-3x^2-2x+1 h=-b/2a
h=-(-2)/2(-3)
h=2/-6= -1/3
y=-3(-1/3)^2-2(-1/3)+1
y=-3(1/9)+2/3+1
y=-1/3+2/3+1
y= 1 1/3
Vertex form : y= -3(x+1/3)^2+1 1/3 h=-b/2a is the most important equation in this process of finding vertex form from standard form.
Connections:
Vertex to Standard- Is the reverse of vertex to standard form. Its best to be able to know how to get back and forth between the two.
Write the Equation- You have to get the vertex point(h,and k) to be able to graph the parabola using y=a(x+h)^2+k.
Graph the Parabola- Vertex and standard form tells how the parabola is to be graphed. It shows what coordinates you need to use, and shows how wide it opens.
Vertex from Standard Form Equation
The Standard form of an equation is y=ax^2+bx+c
The Vertex form of an equation is y=a(x+h)^2+k
Ex. 1
y=-3x^2-2x+1
h=-b/2a
h=-(-2)/2(-3)
h=2/-6= -1/3
y=-3(-1/3)^2-2(-1/3)+1
y=-3(1/9)+2/3+1
y=-1/3+2/3+1
y= 1 1/3
Vertex form : y= -3(x+1/3)^2+1 1/3
h=-b/2a is the most important equation in this process of finding vertex form from standard form.
Connections:
Vertex to Standard- Is the reverse of vertex to standard form. Its best to be able to know how to get back and forth between the two.
Write the Equation- You have to get the vertex point(h,and k) to be able to graph the parabola using y=a(x+h)^2+k.
Graph the Parabola- Vertex and standard form tells how the parabola is to be graphed. It shows what coordinates you need to use, and shows how wide it opens.